Suppose that a firm\'s recent earnings per share and dividend per share are $3.0

Question

Suppose that a firm's recent earnings per share and dividend per share are $3.00 and $1.99, respectively. Both are expected to grow at 11.0 percent. However, the firm's current P/E ratio of 26.0 seems high for this growth rate. The P/E ratio is expected to fall to 21.5 within five years.

Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 19.0 percent required rate. (Do not round your intermediate calculations and round your final answer to 2 decimal places. Omit the "$" sign in your response.)

Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 19.0 percent required rate. (Do not round your intermediate calculations and round your final answer to 2 decimal places. Omit the "$" sign in your response.)

Explanation / Answer

Find the dividends in the next four years:

D1 = $1.99*(1+0.11) = $2.2089

D2 = $2.2089*(1+0.11) = $2.451879

D3 = $2.451879*(1+0.11) = $2.72158569

D4 = $2.72158569*(1+0.11) = $3.0209601159

D5 = $3.0209601159*(1+0.11) = $3.35326572865

Next, to calculate the stock price in year 5:

P5 = (P/E)5*E5 = (P/E)5*E0*(1+g)5 = 21.5*3*1.11^5 = $108.686

Now find the present value of these cash flows using a 19% discount rate to get P0:

P0 = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + (D5+P5)/(1+R)^5

P0 = (2.2089/1.19^1)+(2.451879/1.19^2)+(2.72158569/1.19^3)+(3.0209601159/1.19^4)+((3.35326572865+108.686)/1.19^5)

P0 = $53.6591 = $53.66

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